Applications of Markov Chains in Economic Research

Introduction to Markov Chains in Economics

Markov chains, both in discrete and continuous time, have found extensive applications in various fields within economic research, including game theory, evolutionary dynamics, and repeated games. This article explores several examples and resources that highlight the utility of Markov chains in these areas, providing a comprehensive understanding of their applications in economic modeling.

Markov Chains in Evolutionary Game Theory

In the realm of evolutionary game theory, continuous time Markov chains play a crucial role in analyzing the dynamics of population strategy distributions. By deriving a deterministic mean field model, researchers can predict how the distribution of strategies within a population changes over time. William Sandholm's work, Population Games and Evolutionary Dynamics, provides a detailed exploration of this application, paving the way for more sophisticated models in evolutionary economics.

Markov Chains and Population Dynamics

Markov chains also serve as valuable tools in studying learning and evolution within finite populations. For instance, Lorens Imhof and Drew Fudenberg, in their paper "Imitation Processes with Small Mutations," apply Markov chain approximations to estimate the stationary distribution of a population. This approach helps in understanding how small mutations and imitation processes can influence long-term behavior and stability in a population.

Markov Chains in Repeated Games

The theory of repeated games introduces the concept of Markov perfect equilibria, an equilibrium refinement of subgame perfect equilibria. In this refinement, the strategy of a player in a Markov perfect equilibrium is a mixed strategy that responds to the underlying state of the game. This means that, in a sense, the player's strategy can be viewed as a Markov chain. The application of Markov chains in repeated games is further explored in Economic Origins of Dictatorship and Democracy by James Robinson and Daron Acemoglu, where the authors provide numerous examples from political economy.

Further Reading and Resources

For those interested in delving deeper into the applications of Markov chains in economic research, the following resources are highly recommended: Population Games and Evolutionary Dynamics by William Sandholm Imitation Processes with Small Mutations by Lorens Imhof and Drew Fudenberg Economic Origins of Dictatorship and Democracy by James Robinson and Daron Acemoglu

By exploring these resources, researchers and students can gain a deeper understanding of how Markov chains are used to model and analyze complex economic phenomena, making them essential tools in the economist's toolkit.